What is the limit as x approaches-2+of (-7x)/(x+2) ?

The limit as x approaches-2+of (-7x)/(x+2) is infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

limit as x approaches-2+of (-7x)/(x+2)

x \to - 2 + lim (\frac{- 7 x}{x + 2})

\infty

Solution steps

x \to - 2 + lim (\frac{- 7 x}{x + 2})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= - 7 \cdot x \to - 2 + lim (\frac{x}{x + 2})

Divide by highest denominator power:

\frac{1}{1 + \frac{2}{x}}

= - 7 \cdot x \to - 2 + lim (\frac{1}{1 + \frac{2}{x}})

For

x

approaching

- 2

from the right

, x > - 2 \Rightarrow 1 + \frac{2}{x} < 0

The denominator is a negative quantity approaching 0 from the left

= - 7 (- \infty)

Apply Infinity Property:

- c \cdot (- \infty) = \infty

= \infty

What is the limit as x approaches-2+of (-7x)/(x+2) ?
The limit as x approaches-2+of (-7x)/(x+2) is infinity